Loop groups, Kaluza-Klein reduction and M-theory | Zendy

Aaron Bergman | Zendy; Uday Varadarajan | Zendy

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Loop groups, Kaluza-Klein reduction and M-theory

Author(s) -

Aaron Bergman,

Uday Varadarajan

Publication year - 2005

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2005/06/043

Subject(s) - antisymmetric tensor , principal bundle , associated bundle , bundle , vector valued differential form , supergravity , antisymmetric relation , loop (graph theory) , mathematics , tensor (intrinsic definition) , mathematical physics , pure mathematics , frame bundle , kaluza–klein theory , reduction (mathematics) , tautological line bundle , physics , normal bundle , vector bundle , combinatorics , geometry , gauge theory , supersymmetry , materials science , composite material

We show that the data of a principal G-bundle over a principal circle bundleis equivalent to that of a \hat{LG} = U(1) |x LG bundle over the base of thecircle bundle. We apply this to the Kaluza-Klein reduction of M-theory to IIAand show that certain generalized characteristic classes of the loop groupbundle encode the Bianchi identities of the antisymmetric tensor fields of IIAsupergravity. We further show that the low dimensional characteristic classesof the central extension of the loop group encode the Bianchi identities ofmassive IIA, thereby adding support to the conjectures of hep-th/0203218.Comment: 26 pages, LaTeX, utarticle.cls, v2:clarifications and refs adde

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